Photoelectric lens bench and method for testing optical systems

ABSTRACT

An improved method and apparatus for testing optical systems utilizing one or more cosine potentiometers to correct for errors resulting from perspective and magnification foreshortening or lengthening when off-axis measurements are made.

United States Patent Bruce C. Burdick Pittsford, N.Y.

July 22, 1968 Mar. 30, 1971 Eastman Kodak Company Rochester, N .Y.

Inventor Appl. No. Filed Patented Assignee PHOTOELECTRIC LENS BENCH ANDMETHOD FOR TESTING OPTICAL SYSTEMS 11 Claims, 18 Drawing Figs.

US. Cl 356/124, 356/ I 26 Int. Cl G0lb 9/00 Field of Search 356/124, I26

[5 6] References Cited FOREIGN PATENTS 970,369 9/1964 Great Britain356/124 OTHER REFERENCES Lambert; R. L., Relationship between thesine-wave response and the distribution of energy in the optical imageof a line. Journal of the Optical Society of America Vol. 48, No. 7.Jul. 1958. p. 490- 495.

Fisher; M. R., et al. Laboratory Determination of MTF from Line SpreadFunction. Journal of the Optical Society ofAmerica Vol. 57,No. ll. Nov.1967. p. 1409.

Primary Examiner- Ronald L. Wibert Assistant Examiner-T. MajorAttorneys-Robert W. Hampton and James A. Smith ABSTRACT: An improvedmethod] and apparatus for testing optical systems utilizing one or morecosine potentiometers to correct for errors resulting from perspectiveand magnification foreshortening or lengthening when off-axismeasurements are made.

Patented March so, 1971 4 Sheets-Sheet 1 FIG. 3'

E MA B Y B o c :T .6

FREQUENCY OF TEST OBJECT Patented March 30, 1971 4 Sheets-Sheet 2 FIG.5b

BRUCE C. BURDICK INVEN'I'OR BY QMc/m ATTORNEYS Patented March 30, 1971FIG. 7

TO SHAFT 47 4 Sheets-Sheet 3 TO SHAFT 96 BRUCE C. BURDICK INVENTORQM/22m.

A T TORNE YS Patented March 30, '1971 3,512,939

4 Sheets-Sheet 4 202 20x5 5 20s I L DMDERW FIG IO v 0 v f Min,

FIG. IIC FIG. Ilb FIG. IIC

FIG. IId FIG. Ile FIG. IIf

. J 'fi p fi iie f =i*' BRUCE c. BURDICK INVENTOR ATTOR EYS BACKGROUNDOF THE. INVENTION The present invention relates to methods and apparatusfor testing optical systems, such as lenses, and more particularly toimproved methods and apparatus for measuring the ability of a test lensto transmit various contrast ratios present in a test object or targetto determine the overall quality of the test lens. More specifically,the invention provides for the correction of magnification andperspective foreshortening or lengthening errors which arise during lenstesting with prior art testing methods and apparatus under certaintesting conditions when the the test object is spaced from the opticalaxis of the test lens or positioned in a plane disposed at an angle tothe principal plane of the test lens and the test image.

While applicable to different types of optical testing, the inventionhas particular utility with methods and apparatus which employ a testobject of variable light intensity, such as a lined screen or target,for determining the quality of lens systems. Such a method and apparatusare disclosed, for example, in British Pat. No. 970,369, which issued onSept. 23, 1964, in the name of Lionel R. Baker et a1. As is more fullyex- V plained in said Baker patent, aberrations and other defectsin alens affect the ability of the lens to reproduce spatial-frequencycomponents of a subject or test object. An electronic comparison of suchan object with the corresponding image formed by the test lens yields aresponse, which varies with the spatial frequency and which is afunction of lens quality. This function, sometimes referred to as aModulation Transfer Function (MTF), is usually expressed as thevariation of the lens response with change in spatial frequency.

In. order to determine this function, a test object having a varyingspatial frequency is constructed in an object plane of the test lens,and the corresponding image formed by the test lens is scanned toprovide a test signal. The amplitudes of the test signal, representingthe amplitudes of the image spatialfrequency components, mathematicallyor electrically define the transmission response of the lest lens as afunction of the spatial frequency of the object, and can be used tocalculate the Modulation Transfer Function. While this transfer functioncan be expressed in numerous ways, one widely accepted equationforcalculating the function for any given object spatial-frequency is:MTF=a/b; where a is the peak amplitude of the spatial-frequencycomponents of the image produced by the test lens, and b is the averagevalue of the amplitudes.

In order to analyze the quality of particular optical components, acurve may be plotted illustrating the relationship between the MTF ofthe test lens and the spatial frequency of the test object in the imageplane from spatial frequency to some maximum value. An example of such acurve appears in solid lines on FIG. 3; superimposed upon a similarcurve in dotted lines of the peak amplitude divided by the averageamplitude, of the test object, versus the spatial frequency of the testobject.

To produce an electrical display of the MTF curve for the test lens, asuitable test object of constantly varying spatial frequency can beformed and scanned by orbitally rotating a target disc having an opticalpattern of radially oriented lines and spacings on one side of a firstelongated light-transmitting slit (sometimes referred to as the objectslit or preslit). An image of the test object at the other side of thefirst or object slit is formed by the test lens at a secondlight-transmitting slit (sometimes referred to as the image slit),perpendicularly oriented with respect to' the object slit. Only a smallportion of the spatiai frequency pattern is transmitted through bothslits. This transmitted portion is scanned before a receiver such as aphotomultiplier tube, to generate an electrical signal representing thetest image. As the spatial frequency of the object changes, the maximumor peak amplitudes of the electrical signal representing the imagechange. These peak amplitudes, as well as the average value of theamplitudes, are

used electrically to calculate the MTF of the test lens in accordancewith the formula previously set forth. The signal representing MTF isthen fed to the y axis electrodes of a cathode ray tube or othel'readout device. The x-axis electrodes, on the other hand, receive amodified signal from the target disc representing the actual spatialfrequency of the test object.

Previously known methods and apparatus of this general type are subjectto certain errors which are introduced when off-axis measurements aremade or when the target or test object is oriented at an angle to theprincipal plane of the test lens and test image. For example, as will bedescribed more fully hereinafter, such errors can result frommagnification or perspective foreshortening or lengthening which mayarise when a spatial frequency target, such as an optical line screen,is positioned off the axis of the test lens or in a plane skewed withrespect to the principal-plane of the test lens and test image. Whensuch perspective or magnification foreshortening or lengthening ispresent, the spatial frequency seen through the test lens will not bethe same as the actual spatial frequency of the object, and, unlesscorrected, the spatial frequency represented by the x-axis of thereadout device will not be the same as the spatial frequency actuallyseen through the lens.

SUMMARY OF THE INVENTION An object of the present invention is toprovide an improved method and apparatus, for testing optical systems,which take into account and correct for the above noted errors (to bedescribed more fully hereinafter) that may be introduced when the testobject is positioned off-axis from the test lens or at an angle to thetest image.

In a disclosed embodiment of the invention, one or more functiongenerators may be provided in a system of the described type to modifythe signal representative of the test object or target in accordancewith the angular displacement of the object relative to the principalplane of the lens and test image. More specifically, the signalrepresenting the actual spatial frequency of the target may be modifiedby function generators such as cosine potentiometers whenever the testobject is off-axis or angled with respect to the lens and test image.The signal may thus be modified to correctly represent the spatialfrequency actually seen through the test lens, before the signal is fedto a readout device, such as a plotter or cathode ray tube.

Other objects and advantages will become apparent from the followingdescription of an illustrative preferred embodiment of the invention.

BRIEF DESCRIPTION OF DRAWINGS In the drawings:

FIG. 1 is a plan view of one embodiment of an optical bench inaccordance with the present invention, showing the general features ofthe bench;

FIG. 2 is a side elevational view of the bench depicted in FIG. 1,showing further general features of the bench and also the manner inwhich one or more function generators can be mechanically arranged onthe bench;

FIG. 3 shows a sample curve in a solid line representing the ModulationTransfer Function (peak amplitude divided by average amplitude) of atest lens plotted as the ordinate against the spatial frequency of thetest object as the abcissa; and also, in dotted line, a similar curve ofpeak amplitude divided by average amplitude for the test object;

FIG. 4 is a perspective schematic view of an object forming apparatus inaccordance with the disclosed embodiment of the present invention,showing a target disc and the manner in which it is orbitally rotatedwith respect to a first elongated light transmitting slit;

FIGS. 5a, 5b, and 5c are schematic views of a portion of the objectforming apparatus of FIG. 5, showing the manner in which the spatialfrequency of the object is varied from zero to some maximum value andalso showing the manner in which the object of is scanned, by orbitallyrotating a lined target on one side of an elongated light transmittingslit;

FIG. 6 is a schematic view of the optical bench and associatedelectrical circuitry, showing the same in a mechanical format;

FIG. 7 is a schematic diagram of the circuitry of FIG. 6, showing suchcircuitry in an electrical format;

FIG. ti (sheet l of the drawings) is a diagrammatic view representingthe manner in which perspective error might occur when the object planeis at an angle to the image plane;

FIG. 9 (sheet 4 of the drawings) is a diagrammatic view representing themanner in which magnification error might occur when the test object isdisplaced from the optical axis of the test lens;

HG. W is a schematic diagram of an electrical circuit arrangement forsensing the amplitudes of the test image and for calculating andrepresenting the MTF value of a test lens; and

FIG. lila, lib, llc, lid, lie, and lllf are traces representingelectrical signals at points a, b, c, d, e, and f of the electricalcircuit of H6. 10.

DETAILED DESCRlPTlON OF PREFERRED EMBODIMENTS Referring to FIGS. 1 and 6of the drawings, a preferred embodiment of an optical benchincorporating the present improvement comprises a support or base 1 onwhich are supported an object generator 3, a collimator 5, a lensholding unit 7, a photoelectric reciever 9, and a readout or displaysystem 11 (see FIG. 6). Referring in detail to object generator 3,disclosed most clearly in FIGS. 1 and 45, a source of illumination suchas a tungsten-halogen lamp 113 generates light ray which pass through acondenser or positive lens 15 to illuminate a target of variable lightintensity which may take the form of a circular-lined disc or screen 17.A zoom relay 19 forms an image of the target on an opaque member such asa plate 21 defining an elongated opening or light transmitting slit 23therein which can be rotated for horizontal as well as verticalorientations. One of a plurality of spectral filters 25, mounted on arotatable disc 27, may be placed between light source 13 and slit 23 toalter the spectral composition of the object formed by object generator3.

Target 17 is shown as a glass disc having a radial line screen thereonof approximately l lines per millimeter spatial frequency in the area 29illuminated by lamp 13. The widths of lines 31 on line screen or target17 are tapered, and the lines are located such that, at any given radiusfrom the center 33 of target 17, the width of any line is equal to thespace between the lines. Moreover, the lines in the area 29 aresufficiently distant from center 33 to be effectively parallel.

in order to vary the spatial frequency of the object, target 17 ismounted eccentrically of its center 33 to rotate about axis 37 whichextends through the center of slit 23. As can be seen more clearly inFIGS. 541-50, rotation of the target about axis 37 will generate anobject of varying spatial frequency at slit 23.

As shown on FM]. a, when lines 31 of screen 17 are oriented in the samedirection as slit 23, the spatial frequency will be zero, since lessthan one entire line or space, both of which are wider than the slit,will be visible through the slit. When the target is rotated such thatlines 31 are perpendicular to slit 23, as shown in FIG. 5c, the spatialfrequency will be maximum, and a maximum number of lines and spaces willbe visible through the slit. At intermediate orientations of the target,as represented in FIG. 5b, the spatial frequency will be someintermediate value.

Target 17 is rotatably driven about axis 37 at a constant angularvelocity by means of a synchroneous motor 39, a spur gear 31 and adriven gear 43 upon which the target is mounted by shaft 45. Asdescribed above, such rotation about axis 37 will change the spatialfrequency of the object generated as said object'is viewed from the sideof slit 23 opposite from target 317. While the target is rotated at aconstant angular velocity, the rate of change of thespatial frequency ofthe target varies as a function of the sine or cosine of the angle oftarget rotation, depending on the orientation of silt 23.

in order to obtain a signal representing the spatial frequency of thetest object at any instant in time, a second driven gear 46 engagesfirst driven gear 43 and rotates in response to rotation of gear 43, andtarget 17, about axis 37. Gear 46 is connected via shaft 47 to afunction generator 49, which in the disclosed embodiment takes the formof a sine-cosine potentiometer, such that an electrical signalestablished by the potentiometer will be directly proportional to thespatial frequency of the test object or pattern at slit 23.

As shown in FlG. 7 the sine-cosine potentiometer 49 may comprise a pairof side-wire resistance windings 55 and 57, each of which electricallyhas one end 5ft connected to ground and the other 52 connected to oneterminal of a voltage source, as indicated schematically. A pair ofmovable slider contacts 51 and 53 are connected electrically to fixedcontacts In and n of a single-pole double-throw switch Si, andmechanically to the shaft 47 of gear 45. Contacts 51 and 53 are thuspositioned .along the resistance windings 55 and 57, respectively, inresponse to rotation of the shaft 47, and target 17, and developpotentials at contacts m and n related to the angular position of target17. The windings of resistance 55 is arranged to develop a nonlinearpotential at contact m related to a cosine function of the angle ofrotation of target 17. Similarly, the winding of resistance 5'7 isarranged to develop a nonlinear potential at contact n related to a sinefunction of the angle of rotation of target 17. As will be laterdescribed in connection with operation of the system, a movable contactarrn p of switch S1 may be selectively positioned to introduce eitherthe sine or cosine function into the system.

Sine and cosine potentiometers of the type described are per se wellknown to those skilled in the art and may take various forms other thanthat shown. For example, the resistances 55 and 57 may comprisediametrically opposed circular resistance sections and contact arms 55and 57 could comprise a single arm arranged to selectively cooperatewith either section.

Since the spatial frequency of the test object changes by either a sineor cosine function in proportion to the amount of rotation of target 17,the output of the sine-cosine potentiometer can be used to represent theactual spatial frequency of the test object at any point in time.Provision of a sinecosine potentiometer for this purpose, instead ofonly one or the other, permits an advance of the signal electrically byfor example when slit 23 is advanced mechanically by 90.

As will be described more fully hereinafter, the output signal fromsine-cosine potentiometer 49, representing the ac tual spatial frequencyof the target, may be further modified to compensate for discrepancybetween the spatial frequency of the object as seen through the lens, orthrough the lens from the image plane, and the actual spatial frequencyof the object. The output signal from the sine-cosine potentiometer,after any such further modification can then be fed to the readout ordisplay system i i.

The maximum value of spatial frequency of the test object can be variedby adjustment of relay or zoom lens 19. As the magnification power ofrelay i9 is increased, the maximum spatial frequency of the objectformed by the line grating on the other side of slit 23 will be reduced.

In order to provide for the testing of lenses with objects at infiniteconjugates as well as finite conjugates, the detachable collimator 5 canbe positioned between the test object and test lens. With the objectlocated at the infinity focus of the collimator, the test lens willeffectively see an object at infinity, from which only parallel rayswill enter the test lens. As will be described more fully hereinafter,collimator 5 is mounted for rotation about an axis through the pupil ofthe test lens such that can always be positioned in line between thetest lens and the object generator regardless of the position of theobec'; generator.

The test lens is precisely located with respect to other units of thebench, such as the collimator and the object generator, by means of oneor more interchangeable V-shaped members (r .G. l). Members 59, in turn,are mounted on rectangular plate 61 and slide-bars 63 for adjustablemovement longitudinally of the bench.

in order to generate a meaningful readout indicative of the MT? of thetest lens, the object is scanned to produce an effeet which is detectedby a photoelectric receiver 9, in the form of a photomultiplier in thedisclosed embodiment, which generates an electrical signal representingthe light intensity of the components of the test image. While thisscanning effect could be accomplished in any number of ways, target 17is shown in FIG. 4 as being mounted on shaft 45 for rotation by motor asabout center 33 to scan the object before reciever 9.

From FIGS. l and Sci-5c, it should now be apparent that the frequencycomponents of the object will be constantly moving in a directionlengthwise of slit 23.

In order to limit the image area scanned by the photomultiplier a secondimage slit 67, perpendicular to slit 23, is positionedat the image planein front of receiver 9. Thus the reciever will view only a small squareof the image at any particular instant in time while rotation of target17 about its center 33 will effectively scan the object, and thereforealso the image, before the photomultiplier. At the same time rota tionof target 17 about axis 37 will continuously vary the spa tial frequencyof the test object. Thus, it can be seen that the complex orbitalmovement of the test object serves the first function of varying thespatial frequency of the object and at the same time effectuates ascanning of the test image before the receiver.

Receiver 9 is securely mounted on a base 69 which, in turn is slidablyreceived on rails 71 and slide bar 73 for sliding movement perpendicularto base or support 1. Slide bar 73, in turn, is supported on lead screw75 for movement along rails 7i. Aligning stops 77 and 79 at the ends ofslide bar 73 are precisely spaced such that base 69 can be moved intocontact with stop 79, and knob 81 can be adjusted until image slit 67and reciever 9 are properly oriented with respect to the test image.Thereafter, base 69 can be shifted along slide bar 73 into a positioncontacting stop 77 and such shifting will automatically position asecond unit, such as parfocal microscope E3 in proper position withrespect to the lens.

Referring now in particular to the manner in which off-axis measurementsare made, and to FIGS. 1, 2, and 6, object generator 3 is mounted forpivotal movement about an axis 85 (FIG. ti) directly below the entrancepupil of the test lens. During any such pivotal movement formeasurements at infinite conjugates (i.e. with collimator 5 in operativeposition) an extension oar $7 and collimator bar 89 maintain objectgenerator 3 at a predetermined length from axis 85 through the lenspupil.

While not required by the present invention, object generator 3 can beselectively mounted for movement on either of two slideways 911 and 93.Slideway Ell permits rectilinear movement of the object generator in aplane parallel to the principal plane of the test lens, and may be usedfor measurements at finite conjugates, while slideway 93 permits arcuatemovement of the generator, and is usually used for measurements atfinite conjugates. Collimator 5, when in use, is also mounted forpivotal movement about the same axis 85 below the test lens of theobject generator. Furthermore, the collimator is attached to collimatorbar 89 and extension bar '87 in such a manner that the collimator willhave the same angular position with respect to the lens as the objectgenerator.

n FIGS. 1. and 9, object generator 3 and receiver 9 are shown in severaldifferent operative positions. A first position (2, shown in solidlines, is that normally taken by the object generator and the receiverwhen the lens is tested at finite or infinite conjugates on the opticalaxis of the test lens. Position 15, in dotted. lines, is the positiontaken by the object generator and reciever when the lens is tested forfinite conjugates (without collimator off the optical axis of the testlens. Position c, also shown in dotted lines, is taken by the opticalgenerator and receiver for tests at infinite conjugates off the opticalaxis of the test lens.

it should be noted that receiver 9 and image slit 57 are usuallyoriented in planes parallel to the principal plane of the rest of thelens to assure that the test image is sensed in a plane parallel to theprincipal plane of the test lens. In this manner the ordinary use of thelens in a camera with a flat film plane is closely simulated. Target 17and object or preslit 23, on the other hand, may be in planes angularlyoriented with respect to the lens. Such orientations, for example, areshown at position 0, which is the normal position for measurementsoff-axis at infinite conjugates. This angular and off-axis position isrequired for off-axis measurements .at infinite conjugates because ofthe angular field limitations and the criticality of the infinity focusof collimator 5.

As previously mentioned, the angular relationship between the plane ofthe object (as defined by the plane of the target) and the plane-of theimage (as defined by the plane of the receiver) introduces perspectiveerror, while the olf-axis position of the object with respect to thelens when test are made at infinite conjugates introduces magnificationerror.

Perspective error has been found to be function of the cosine of theangle between the object plane and the image or projection plane, andresults from the fact that the test lens images the target or object ona plane which is not parallel to the object plane. Thus, the cycles ofthe target are spread out over an angled projection plane which islonger than a parallel projection plane by the secant of the angle; orthe spatial frequency is diminished by the cosine of the angle.

This phenomenon is shown diagrammatically on FIG. 8, wherein line drepresents the object plane, line 2 represents the image plane, andlines g-k represent the peak amplitudes of the test object in the areaof the image plane. From FIG. 8, it can be seen that the spatialfrequency, which varies inversely as the distance between the pealtamplitudes g-k of the image, will be less when taken along plane f thanwhen taken along plane e. With the particular apparatus shown, theobject and image planes are always parallel when measurements at finiteconjugates are made and no perspective error is present. However, atinfinite conjugates, the object and image plane may be skewed withrespect to each other and perspective error results.

Magnification error, on the other hand, has been found to be a functionof the cosine of the angle by which the test object is displaced fromthe optical axis of the test lens. This phenomenon is showndiagrammatically in FIG. 9. For finite conjugates on-axis (position a)the magnification of the test lens is proportional to distance 0L(object to lens) divided by distance LI (lens to image). For finiteconjugates off-axis (position b) the magnification of the test lens isproportional to distance 0'L' divided by distance LT'. With theapparatus shown, this proportion of llL/LI or O'L'l U1 is constant forall measurement at finite conjugates, i.e. when the object and receiverare in positions a or b, and no magnification error is present. Howeverfor infinite conjugates the magnification of the test lens isproportional to distance 0"C" (object to collimator) divided by distanceL"l". In this case, distance 0"C" is constant because the object mustalways be located at the infinity focus of the collimator, but distanceL"l" changes as the object generator is moved or displaced off theoptical axis. Therefore, magnification error is introduced by suchoff-axis positioning.

in the apparatus described above, perspective error is present only whenthe object or preslit is horizontally oriented; that its, when theamplitudes of the frequency components vary in direction of increasingdistance between object and image. Magnification error, on the otherhand, does not depend upon the orientation of slit .23.

It should now be recognized that perspective error occurs whenever theobject and image plane are angled with respect to each other such thatthe amplitudes of the frequency components of the object vary in thedirection of increasing distance between object and image, andmagnification error occurs whenever the object is displaced from theoptical axis of the test lens and a collimator is positioned between theobject and the image. With a bench of the type described, bothperspective and magnification error occur when off-axis measurements aremade at infinite conjugates with the object slit horizontally oriented.Magnification error will occur when offaxis measurements are made atinfinite conjugates with the object slit vertically oriented. Neithererror is present when measurements are made at finite conjugates or onthe optical axis of the test lens.

in order to correctly account for both of the abovedescribed errors, twofunction generators such as cosine potentiometers 95 and 97 (see H68. 6and 7) are mounted below the test lens entrance pupil. Cosinepotentiometer 95 comprises a slide-wire resistance winding 1103electrically connected at one end to ground and at the other end to acontact q comprising one of the terminals of a single-pole doublethrowswitch S2. A movable contact arm s of switch S2 is electricallyconnected to the movable contact arm p of switch S1 and can bepositioned to electrically connect contact q to sinecosine potentiometer49 for transmitting the output of potentiometer 49 to cosinepotentiometer 95. Movable contact arm s can also be positioned inengagement with a contact r comprising the other terminal of switch S2,in order to bypass cosine potentiometer 95 for reasons to becomeapparent hereinafter. Movable slider contact 99 of cosine'potentiometer95 is electrically connected to a contact arm w movable between contactt and u of a third single-pole double-throw switch S3. Slider contact 99is movable along winding 103 in response to rotation of shaft 96 andthereby develops a potential at the contact arm w of switch S3 which isrelated to the angular position of shaft 96. The resistance of winding1% is arranged so that the potential change introduced by potentiometer95 will be nonlinear and a cosine function of the angle of rotation ofshaft 96 about axis 85.

in a similar manner, cosine potentiometer 97 comprises a slide wireresistance winding 195 electrically connected at one end to ground andat the other end to a contact t comprising one of the terminals ofswitch S3. Movable contact arm w of switch S3 is electrically connectedto slider contact 99 of potentiometer 95 and can be positioned toelectrically connect contact I to slide 99 of cosine potentiometer 95for transmitting the output of potentiometer 95 to potentiometer 97.Movable contact arm w can also be positioned in engagement with acontact 14 comprising the other terminal switch S3 in order to bypasspotentiometer 97-for reasons to become more apparent hereinafter.Movable slider 101 of cosine potentiometer 97 is electrically connectedto the x-axis plates of a readout device it, and is movable alongwinding 165 in response to rotation of shaft 96 to develop a potentialwhich is related to the angular position of shaft 96. The resistance ofwinding 105 is arranged so that the potential change resulting frompotentiometer 97 will be nonlinear and a cosine function of the angle ofrotation of shaft 96 about axis 85.

in the disclosed embodiment, the angular movement of the potentiometerslides will be proportional not only to the displacement of the objectgenerator off the optical axis of the test lens but also to the angularrotation of the object plane with respect to the image plane. Thus, thefirst potentiometer 95 can be used to correct for perspective error,which is a function of the angle between the object plane the imageplane, while the second potentiometer 97 can be used to correct formagnification error, which is a function of the amount of off-axisdisplacement of the object with respect to the optical axis of the testlens.

The signal from the sine-cosine potentiometer 49 representing the actualspatial frequency of the test object, can be fed by switching means Siand S2 to one or both of said cosine potentiometers or both cosinepotentiometers can be entirely bypassed. When used, the one cosinepotentiometer modifies the input as function of the cosine of the angleby which the test object is displaced from the optical axis of the testlens,

while the other cosine potentiometer modifies the signal as a functionof the cosine of the angle by which the object plane is skewed withrespect to the image plane. Since the errors introduced by off-axismeasurements vary by these same functions, the outputs from thepotentiometers will represent the spatial frequency actually seen by thetest lens and receiver.

in the case where object slit 23 is horizontally oriented, and off-axismeasurements are made at infinite conjugates, switches S2 and S3 are inthe positions shown on FIGS. 6 and 7, engaging contacts q and 1. Thus,both potentiometers and 97 are connected in series to correct for bothperspective and magnification error. When object slit 23 is verticallyoriented, switch S3 can be moved to contact 14 such that onlypotentiometer 95 is used only magnification error is corrected for. Whenthe object and image are in parallel planes and the object is on theoptical axis of the test lens, contact arm s of switch S2 is moved tocontact r to bypass both potentiometers. Similarly, when the collimator5 is removed, and measurements are made at finite conjugates, contactarm s is moved to contact r to bypass both potentiometers. It should beapparent to those skilled in the art that potentiometers could beeffectively bypassed without switches Sl and S2, by moving slides 99 and101 to the ends of windings 103 and 105 remote from ground. L

In order to provide a visual readout, the electrical signal representingthe intensity components of the image formed by the test lens is fed toan electrical calculator or computer where the MTF is calculated bydividing the peak amplitudes by the average amplitude. This MTF signalis then fed, for example, to the y-axis electrodes of a mechanicalplotter. The electrical signal representing the spatial frequency of thetest object, as seen by the test lens, if fed to x-axis electrodes ofthe plotter, presenting on the plotter a visual image of the ModulationTransfer Function of the test lens over a range of spatial frequenciesof the test object. In a similar manner the transfer function can bevisually presented on the screen of a cathode ray oscilloscope.

Referring to FIG. 10 there is shown a block diagram of the circuitry ofthe instruments for sensing the intensity components of the test imageand calculating the MTF of the test lens. The image formed by the testlens at slit 67 is scanned in the manner previously described before aphotocell (photovoltaic, photoresistive or phototransistive), which inthe embodiment shown is is a photomultiplier. The photocell orphotomultiplier 2t)! generates an output signal representing the imagewhich is fed to a preamlifier 2ll2. Part of the output of amplifier 202is fed to a low pass network consisting of resistor 293 and capacitor204. The other part of the output of amplifier 292 is fed to band passfilter 2%5 which is here illustrated as being in series with capacitor2% to show that band pass filter 295 passes AC only. It is, of course,to be understood that capacitor 206 is not actually a circuit component,but represents a situation that only alternating current will passthrough band pass filter 205. The low pass filter consisting of resistor203 and capacitor 204 causes the input to DC amplifier 207 to besubstantially the average or DC level of the output amplifier 202. Thepurpose of band pass filter 205 is, of course, to rid the signal ofnoise and harmonics. A wave form of the output of amplifier 202 asmeasured at point a is shown in FIG. 11a. The output of the band passfilter as measured at point b is shown in FIG. lib. The output of bandpass filter 205 together with the output of DC amplifier 207 is sent toreconstructing inverter 20% which replaces the DC level which is lostwhen the signal went through the band pass filter 205. The output ofinverter 208 as measured at point c is shown in FIG. lie. The signal isthen reinverted by inverter 209 and the peak detected by a peak detectornetwork consisting of diode 210 and capacitor 211. Therefore, the signalat terminal d represents the envelope of the peaks of the originalsignal wave form and is shown in H6. llld. The output of the peakdetector is fed to follower amplifier 212 which is in turn fed to thedividend terminal of divider 213. The division terminal of divider 213is fed by the average or DC level output of amplifier 2437. The output etherefore of divider 213 is the quotient of the output of amplifier 212divided by the output of amplifier 2m and is shown in HQ. lie. Finally,the output is amplified by output amplifier 214 to produce the final orterminal wave the form of which is shown in FlG. 11 f.

The above configuration is necessary because divider 213 will operateonly in a very restricted range, i.e., the dividend terminal of thedivider must be maintained within a certain very narrow range. For thisreason, a DC level is reinserted onto the signal through reconstructinginverter 2% in order that the minimum output from follower 212 willnever be left below the minimum for which divider 213 retains itsaccuracy.

it can therefore be seen that the above circuit provides the desiredModulation Transfer Function (MTF) of the test lens over a range ofspatial frequencies of the test object.

Referring now to the overall operation of the optical bench and methodin accordance with the present invention, measurements are made on-axisat finite conjugates with the object generator and receiver in positionsa as shown on FIGS. 1 and 9. Since no magnification or perspective erroris present, contact arm s is moved to engage contact r of switch S2 tobypass both correction potentiometers 95 and 97. Target I7 is orbitallyrotated about its center 33 and also about'axis 37 to generate and scanan object of varying spatial frequency at object slit 23. The imagetransmitted by the test lens is sensed by receiver 9 and the MTF of thetest lens is electrically calculated by dividing the maximum value ofthe amplitudes of the image by the average value of the amplitudes asthe spatial frequency of the object is varied. Measurements off-axis atfinite conjugates are made in a similar manner with the object generatorand receiver in positions b. However, measurements off-axis at infiniteconjugates will not be accurate when the object generator and receiverare in positions c and when a collimator is used, unless magnificationand perspective error are taken into account. in order to take sucherror into account, contact arm s of switch S2 is moved into engagementwith contact q. Further, when object slit 23 is horizontally oriented,contact arm w is moved into engagement with contact t. In this manner,magnification error and perspective error are corrected for wheneverpresent.

The invention has been described in detail with particular reference topreferred embodiments thereof, but it will be understood that variationsand modifications can be effected within the spirit and scope of theinvention as described hereinabove and as defined in the appendedclaims.

lclaim:

l. in a method for testing the response of an optical system, whichincludes the steps of: positioning a spatial-frequency target at atarget plane; imaging the target by the optical system under test at animage plane angled with respect to the target plane such that theamplitude of the spatial-frequency target image varies along thedirection of increasing distance between the target plane and the imageplane; and forming a signal representing the actual spatial frequency ofthe target; the improvement comprising the step of correcting the signalrepresenting the actual spatial frequency of the target to compensatefor perspective error resulting from the angle between the target planeand the image plane.

2. in a method of testing the response of an optical system at aninfinite conjugate, which includes the steps of: positioning aspatial-frequency target at a location displaced from the optical axisof the optical system under test; and forming a signal indicative of theactual spatial frequency of the target; the improvement comprising thestep of correcting the signal representing the actual spatial frequencyof the target to compensate for magnification error resulting from suchdisplacement of the target from the optical axis of the optical system.

in a method of testing the response of an optical component whichincludes the steps of: positioning a spatialfrequency target at a targetplane at an infinite conjugate with respect to the optical component;imaging the target by the optical component under test at an image planeangled with respect to the target plane such that the amplitudes of thetarget image vary along the direction of increasing distance between theobject plane and the image plane; and generating a response representingthe actual spatial frequency of the target; the improvement comprisingthe steps of correcting the response representing the actual spatialfrequency of the target to compensate for perspective error resultingfrom the angle between the target plane and the image plane, andcorrecting the response representing the actual spatial frequency of thetarget to compensate for magnification error resulting from thedisplacement of the target from the optical axis of the opticalcomponents.

4. A method of testing an optical imaging means having an optical axis,which includes the steps of:

positioning a variable intensity test object of determinable spatialfrequency a predetermined distance off said optical axis; forming a testimage of the test object by means of said imaging means;photoelectrically scanning said test image to establish a firstelectrical signal representing the test image; establishing a secondelectrical signal representing the actual spatial frequency of the testobject; modifying said second signal as a function of said predeterminedoff-axis distance to correct for error due to such off-axis distance;and graphically plotting said second signal against said first signalwhile varying the frequency of said test object. 5. A method of testingoptical systems having a principal plane, comprising:

forming a variable intensity test object of determinable spatialfrequency at a plane angularly oriented with respect to the principalplane of a system under test; forming a test image of the test object ina plane parallel to the principal plane of the system by means of thesystem; detecting the test image with a photoelectric receiver to forman electrical signal representing the test image; generating anelectrical signal representing the actual spatial frequency of the testobject; modifying said signal representing the actual spatial frequencyof the test object by a function of the angle between the object planeand the: image plane whenever.

amplitudes of the test object vary along the direction of increasingdistance between the object plane and the image plane, to correct forerror due to such angle; and

visually displaying said signal representing the test image and saidmodified signal representing the spatial frequency of the test object.

6. A method of testing the response of an optical system having anoptical axis and a principal plane, comprising:

forming a variable intensity test object of determinable spa tialfrequency off the optical axis and at plane angularly oriented withrespect to the principal plane of an optical system under test;

forming a test image of the test object, in a plane parallel to theprincipal plane of the optical system, by means of the optical system;

detecting the test image with a photoelectric receiver to form anelectrical signal representing the test image;

generating a signal representing the actual spatial frequency of thetest object;

modifying said signal representing the actual spatial frequency of thetest object as a function of the angle between the object plane and theimage plane whenever the amplitudes of the test object vary along thedirection of increasing distance between the object and image planes andalso by the amount the object is off axis from the optical axis of theoptical system, to correct for error due to such angle and off-axisamount; and

comparing said signal representing the test image with the modifiedsignal representing the spatial frequency of the test object.

7. An optical bench for testing lens systems having an optical axis,said bench comprising:

means including one or more lines target discs for forming a test objectof determinable and variable spatial frequency;

means for generating a signal representing the actual spatial frequencyof said test object;

7 means for supporting a lens system to be tested;

means for adjusting the position of the test object relative to the lenssystem for locating the test object off the optical axis of the lenssystem; and

at least one function generator operatively connected to said signalgenerating means for altering said signal to correct for changes in thespatial frequency of the test object as imaged by the lens system whichare due to the test object being located off the optical axis of thelens system.

8. An optical bench for testing lens systems having an optical axis, inaccordance with claim 7, wherein said function generator is a cosinepotentiometer.

Q. An optical bench for testing lens systems having an optical axis,comprising:

means including at least one lined target for forming a test object ofdeterminable and variable spatial frequency in an object plane;

means for establishing a signal representing the actual spatialfrequency of said test object;

holding means for locating a lens system to be tested;

means defining an image plane at which the lens system forms an image ofthe test object;

receiving means for sensing an image of the test object at the imageplane;

means for adjusting the test object with respect to the test image toestablish an angle between the object plane and the image plane; and

at least one function generator operatively connected to said signalgenerating means for altering said signal to compensate for s changes inthe spatial frequency of the test image which are due to the anglebetween the object plane and the image plane.

ll). in an optical bench for testing optical systems having an opticalaxis and a principal plane, and including a lined test object ofvariable spatial frequency, electrical means for generating a signalvoltage proportional to the variable spatial frequency, means fororienting the test object off the optical axis of an optical systemunder test and in a plane oriented at an angle to the principal plane ofthe optical system, the improvement comprising at least onepotentiometer means operatively associated with the electrical signalgenerating means for altering the signal voltage bya cosine function tocorrect for perspective error resulting from the angle between theobject plane and the principal plane and magnification error resultingfrom the off-axis position of the test object with respect to theoptical axis of the optical system.

11. An optical bench; for testing a lens system having an optical axisand a principal plane, comprising:

at least one lined screen defining a plane and for forming a test objectof variable spatial frequency;

means for developing a first electrical output indicative of the spatialfrequency of the test object;

means for supporting the lens system with the optical axis of the lenssystem displaced at an angle from the test object and with the principalplane of the lens system oriented at an angle with respect to the planeof said screen, said support means being located with respect to thetest object such that the lens system supported thereby will form a testimage of the test object;

a photoelectric receiver for sensing a test image formed by the lenssystem in an image plane parallel to the principal plane of the lenssystem and for developing a second electrical output indicative of thetest image in said image plane;

a first cosine potentiometer electrically connected to said means fordeveloping said first electrical output and having a resistance elementand a contact movable relative to said element to develop an outputpotential related to a function of the cosine of the angle by which theprincipal plane of the lens system is oriented with respect to the planeof said screen;

a second cosine potentiometer electrically connected to said firstpotentiometer, and having a second resistance element and a contactmovable relative to said element to develop an output potential relatedto a function of the cosine of the angular amount by which the opticalaxis of the lens system is displaced from the object;

first switch means for electrically connecting said first potentiometerto said means for developing said first electrical output to correct forperspective error resulting from the angle by which the principal planeof the lens system is oriented with respect to the plane of said screen;and

second switch means for electrically connecting said secondpotentiometer to said first potentiometer to correct for magnificationerror resulting from the angular amount by which the optical axis of thelens system is displaced from the object.

1. In a method for testing the response of an optical system, whichincludes the steps of: positioning a spatial-frequency target at atarget plane; imaging the target by the optical system under test at animage plane angled with respect to the target plane such that theamplitude of the spatial-frequency target image varies along thedirection of increasing distance between the target plane and the imageplane; and forming a signal representing the actual spatial frequency ofthe target; the improvement comprising the step of correcting the signalrepresenting the actual spatial frequency of the target to compensatefor perspective error resulting from the angle between the target planeand the image plane.
 2. In a method of testing the response of anoptical system at an infinite conjugate, which includes the steps of:positioning a spatial-frequency target at a location displaced from theoptical axis of the optical system under test; and forming a signalindicative of the actual spatial frequency of the target; theimprovement comprising the step of correcting the signal representingthe actual spatial frequency of the target to compensate formagnification error resulting from such displacement of the target fromthe optical axis of the optical system.
 3. In a method of testing theresponse of an optical component which includes the steps of:positioning a spatial-frequency target at a target Plane at an infiniteconjugate with respect to the optical component; imaging the target bythe optical component under test at an image plane angled with respectto the target plane such that the amplitudes of the target image varyalong the direction of increasing distance between the object plane andthe image plane; and generating a response representing the actualspatial frequency of the target; the improvement comprising the steps ofcorrecting the response representing the actual spatial frequency of thetarget to compensate for perspective error resulting from the anglebetween the target plane and the image plane, and correcting theresponse representing the actual spatial frequency of the target tocompensate for magnification error resulting from the displacement ofthe target from the optical axis of the optical components.
 4. A methodof testing an optical imaging means having an optical axis, whichincludes the steps of: positioning a variable intensity test object ofdeterminable spatial frequency a predetermined distance off said opticalaxis; forming a test image of the test object by means of said imagingmeans; photoelectrically scanning said test image to establish a firstelectrical signal representing the test image; establishing a secondelectrical signal representing the actual spatial frequency of the testobject; modifying said second signal as a function of said predeterminedoff-axis distance to correct for error due to such off-axis distance;and graphically plotting said second signal against said first signalwhile varying the frequency of said test object.
 5. A method of testingoptical systems having a principal plane, comprising: forming a variableintensity test object of determinable spatial frequency at a planeangularly oriented with respect to the principal plane of a system undertest; forming a test image of the test object in a plane parallel to theprincipal plane of the system by means of the system; detecting the testimage with a photoelectric receiver to form an electrical signalrepresenting the test image; generating an electrical signalrepresenting the actual spatial frequency of the test object; modifyingsaid signal representing the actual spatial frequency of the test objectby a function of the angle between the object plane and the image planewhenever amplitudes of the test object vary along the direction ofincreasing distance between the object plane and the image plane, tocorrect for error due to such angle; and visually displaying said signalrepresenting the test image and said modified signal representing thespatial frequency of the test object.
 6. A method of testing theresponse of an optical system having an optical axis and a principalplane, comprising: forming a variable intensity test object ofdeterminable spatial frequency off the optical axis and at planeangularly oriented with respect to the principal plane of an opticalsystem under test; forming a test image of the test object, in a planeparallel to the principal plane of the optical system, by means of theoptical system; detecting the test image with a photoelectric receiverto form an electrical signal representing the test image; generating asignal representing the actual spatial frequency of the test object;modifying said signal representing the actual spatial frequency of thetest object as a function of the angle between the object plane and theimage plane whenever the amplitudes of the test object vary along thedirection of increasing distance between the object and image planes andalso by the amount the object is off axis from the optical axis of theoptical system, to correct for error due to such angle and off-axisamount; and comparing said signal representing the test image with themodified signal representing the spatial frequency of the test object.7. An optical bench for testing lens systems having an optical axis,said bench comPrising: means including one or more lines target discsfor forming a test object of determinable and variable spatialfrequency; means for generating a signal representing the actual spatialfrequency of said test object; means for supporting a lens system to betested; means for adjusting the position of the test object relative tothe lens system for locating the test object off the optical axis of thelens system; and at least one function generator operatively connectedto said signal generating means for altering said signal to correct forchanges in the spatial frequency of the test object as imaged by thelens system which are due to the test object being located off theoptical axis of the lens system.
 8. An optical bench for testing lenssystems having an optical axis, in accordance with claim 7, wherein saidfunction generator is a cosine potentiometer.
 9. An optical bench fortesting lens systems having an optical axis, comprising: means includingat least one lined target for forming a test object of determinable andvariable spatial frequency in an object plane; means for establishing asignal representing the actual spatial frequency of said test object;holding means for locating a lens system to be tested; means defining animage plane at which the lens system forms an image of the test object;receiving means for sensing an image of the test object at the imageplane; means for adjusting the test object with respect to the testimage to establish an angle between the object plane and the imageplane; and at least one function generator operatively connected to saidsignal generating means for altering said signal to compensate for schanges in the spatial frequency of the test image which are due to theangle between the object plane and the image plane.
 10. In an opticalbench for testing optical systems having an optical axis and a principalplane, and including a lined test object of variable spatial frequency,electrical means for generating a signal voltage proportional to thevariable spatial frequency, means for orienting the test object off theoptical axis of an optical system under test and in a plane oriented atan angle to the principal plane of the optical system, the improvementcomprising at least one potentiometer means operatively associated withthe electrical signal generating means for altering the signal voltageby a cosine function to correct for perspective error resulting from theangle between the object plane and the principal plane and magnificationerror resulting from the off-axis position of the test object withrespect to the optical axis of the optical system.
 11. An optical bench,for testing a lens system having an optical axis and a principal plane,comprising: at least one lined screen defining a plane and for forming atest object of variable spatial frequency; means for developing a firstelectrical output indicative of the spatial frequency of the testobject; means for supporting the lens system with the optical axis ofthe lens system displaced at an angle from the test object and with theprincipal plane of the lens system oriented at an angle with respect tothe plane of said screen, said support means being located with respectto the test object such that the lens system supported thereby will forma test image of the test object; a photoelectric receiver for sensing atest image formed by the lens system in an image plane parallel to theprincipal plane of the lens system and for developing a secondelectrical output indicative of the test image in said image plane; afirst cosine potentiometer electrically connected to said means fordeveloping said first electrical output and having a resistance elementand a contact movable relative to said element to develop an outputpotential related to a function of the cosine of the angle by which theprincipal plane of the lens system is oriented with respect to the planeoF said screen; a second cosine potentiometer electrically connected tosaid first potentiometer, and having a second resistance element and acontact movable relative to said element to develop an output potentialrelated to a function of the cosine of the angular amount by which theoptical axis of the lens system is displaced from the object; firstswitch means for electrically connecting said first potentiometer tosaid means for developing said first electrical output to correct forperspective error resulting from the angle by which the principal planeof the lens system is oriented with respect to the plane of said screen;and second switch means for electrically connecting said secondpotentiometer to said first potentiometer to correct for magnificationerror resulting from the angular amount by which the optical axis of thelens system is displaced from the object.